The colour and pattern changing abilities of octopus, squid and cuttlefish via chromatophore neuro-muscular organs are unparalleled. Cuttlefish and octopuses also have a unique muscular hydrostat system in their skin. When expressed, dermal bumps called papillae disrupt body shape and imitate the fine texture of surrounding objects, yet the control system is unknown. Here we report for papillae: (i) the motoneurons and the neurotransmitters that control activation and relaxation, (ii) a physiologically fast expression and retraction system, and (iii) a complex of smooth and striated muscles that enables long-term expression of papillae through sustained tension in the absence of neural input. The neural circuits controlling acute shape-shifting skin papillae in cuttlefish show homology to the iridescence circuits in squids. The sustained-tension in papillary muscles for long-term camouflage utilizes muscle heterogeneity, and points toward the existence of a "catch-like" mechanism that would reduce the necessary energy expenditure.